/*
 * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

package java.util;

/**
 * This class implements the Dual-Pivot Quicksort algorithm by
 * Vladimir Yaroslavskiy, Jon Bentley, and Josh Bloch. The algorithm
 * offers O(n log(n)) performance on many data sets that cause other
 * quicksorts to degrade to quadratic performance, and is typically
 * faster than traditional (one-pivot) Quicksort implementations.
 *
 * All exposed methods are package-private, designed to be invoked
 * from public methods (in class Arrays) after performing any
 * necessary array bounds checks and expanding parameters into the
 * required forms.
 *
 * @author Vladimir Yaroslavskiy
 * @author Jon Bentley
 * @author Josh Bloch
 * @version 2011.02.11 m765.827.12i:5\7pm
 * @since 1.7
 */
final class DualPivotQuicksort {

  /**
   * Prevents instantiation.
   */
  private DualPivotQuicksort() {
  }

    /*
     * Tuning parameters.
     */

  /**
   * The maximum number of runs in merge sort.
   */
  private static final int MAX_RUN_COUNT = 67;

  /**
   * The maximum length of run in merge sort.
   */
  private static final int MAX_RUN_LENGTH = 33;

  /**
   * If the length of an array to be sorted is less than this
   * constant, Quicksort is used in preference to merge sort.
   */
  private static final int QUICKSORT_THRESHOLD = 286;

  /**
   * If the length of an array to be sorted is less than this
   * constant, insertion sort is used in preference to Quicksort.
   */
  private static final int INSERTION_SORT_THRESHOLD = 47;

  /**
   * If the length of a byte array to be sorted is greater than this
   * constant, counting sort is used in preference to insertion sort.
   */
  private static final int COUNTING_SORT_THRESHOLD_FOR_BYTE = 29;

  /**
   * If the length of a short or char array to be sorted is greater
   * than this constant, counting sort is used in preference to Quicksort.
   */
  private static final int COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR = 3200;

    /*
     * Sorting methods for seven primitive types.
     */

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(int[] a, int left, int right,
      int[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          int t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    int[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new int[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      int[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(int[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          int ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          int a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        int last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      int t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      int t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      int t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      int t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      int pivot1 = a[e2];
      int pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        int ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          int ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = pivot1;
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      int pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        int ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = pivot;
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(long[] a, int left, int right,
      long[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          long t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    long[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new long[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      long[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(long[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          long ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          long a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        long last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      long t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      long t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      long t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      long t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      long pivot1 = a[e2];
      long pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        long ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          long ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = pivot1;
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      long pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        long ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = pivot;
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(short[] a, int left, int right,
      short[] work, int workBase, int workLen) {
    // Use counting sort on large arrays
    if (right - left > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
      int[] count = new int[NUM_SHORT_VALUES];

      for (int i = left - 1; ++i <= right;
          count[a[i] - Short.MIN_VALUE]++
          ) {
        ;
      }
      for (int i = NUM_SHORT_VALUES, k = right + 1; k > left; ) {
        while (count[--i] == 0) {
          ;
        }
        short value = (short) (i + Short.MIN_VALUE);
        int s = count[i];

        do {
          a[--k] = value;
        } while (--s > 0);
      }
    } else { // Use Dual-Pivot Quicksort on small arrays
      doSort(a, left, right, work, workBase, workLen);
    }
  }

  /**
   * The number of distinct short values.
   */
  private static final int NUM_SHORT_VALUES = 1 << 16;

  /**
   * Sorts the specified range of the array.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  private static void doSort(short[] a, int left, int right,
      short[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          short t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    short[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new short[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      short[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(short[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          short ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          short a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        short last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      short t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      short t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      short t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      short t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      short pivot1 = a[e2];
      short pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        short ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          short ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = pivot1;
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      short pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        short ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = pivot;
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(char[] a, int left, int right,
      char[] work, int workBase, int workLen) {
    // Use counting sort on large arrays
    if (right - left > COUNTING_SORT_THRESHOLD_FOR_SHORT_OR_CHAR) {
      int[] count = new int[NUM_CHAR_VALUES];

      for (int i = left - 1; ++i <= right;
          count[a[i]]++
          ) {
        ;
      }
      for (int i = NUM_CHAR_VALUES, k = right + 1; k > left; ) {
        while (count[--i] == 0) {
          ;
        }
        char value = (char) i;
        int s = count[i];

        do {
          a[--k] = value;
        } while (--s > 0);
      }
    } else { // Use Dual-Pivot Quicksort on small arrays
      doSort(a, left, right, work, workBase, workLen);
    }
  }

  /**
   * The number of distinct char values.
   */
  private static final int NUM_CHAR_VALUES = 1 << 16;

  /**
   * Sorts the specified range of the array.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  private static void doSort(char[] a, int left, int right,
      char[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          char t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    char[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new char[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      char[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(char[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          char ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          char a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        char last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      char t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      char t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      char t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      char t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      char pivot1 = a[e2];
      char pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        char ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          char ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = pivot1;
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      char pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        char ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = pivot;
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }

  /**
   * The number of distinct byte values.
   */
  private static final int NUM_BYTE_VALUES = 1 << 8;

  /**
   * Sorts the specified range of the array.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   */
  static void sort(byte[] a, int left, int right) {
    // Use counting sort on large arrays
    if (right - left > COUNTING_SORT_THRESHOLD_FOR_BYTE) {
      int[] count = new int[NUM_BYTE_VALUES];

      for (int i = left - 1; ++i <= right;
          count[a[i] - Byte.MIN_VALUE]++
          ) {
        ;
      }
      for (int i = NUM_BYTE_VALUES, k = right + 1; k > left; ) {
        while (count[--i] == 0) {
          ;
        }
        byte value = (byte) (i + Byte.MIN_VALUE);
        int s = count[i];

        do {
          a[--k] = value;
        } while (--s > 0);
      }
    } else { // Use insertion sort on small arrays
      for (int i = left, j = i; i < right; j = ++i) {
        byte ai = a[i + 1];
        while (ai < a[j]) {
          a[j + 1] = a[j];
          if (j-- == left) {
            break;
          }
        }
        a[j + 1] = ai;
      }
    }
  }

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(float[] a, int left, int right,
      float[] work, int workBase, int workLen) {
        /*
         * Phase 1: Move NaNs to the end of the array.
         */
    while (left <= right && Float.isNaN(a[right])) {
      --right;
    }
    for (int k = right; --k >= left; ) {
      float ak = a[k];
      if (ak != ak) { // a[k] is NaN
        a[k] = a[right];
        a[right] = ak;
        --right;
      }
    }

        /*
         * Phase 2: Sort everything except NaNs (which are already in place).
         */
    doSort(a, left, right, work, workBase, workLen);

        /*
         * Phase 3: Place negative zeros before positive zeros.
         */
    int hi = right;

        /*
         * Find the first zero, or first positive, or last negative element.
         */
    while (left < hi) {
      int middle = (left + hi) >>> 1;
      float middleValue = a[middle];

      if (middleValue < 0.0f) {
        left = middle + 1;
      } else {
        hi = middle;
      }
    }

        /*
         * Skip the last negative value (if any) or all leading negative zeros.
         */
    while (left <= right && Float.floatToRawIntBits(a[left]) < 0) {
      ++left;
    }

        /*
         * Move negative zeros to the beginning of the sub-range.
         *
         * Partitioning:
         *
         * +----------------------------------------------------+
         * |   < 0.0   |   -0.0   |   0.0   |   ?  ( >= 0.0 )   |
         * +----------------------------------------------------+
         *              ^          ^         ^
         *              |          |         |
         *             left        p         k
         *
         * Invariants:
         *
         *   all in (*,  left)  <  0.0
         *   all in [left,  p) == -0.0
         *   all in [p,     k) ==  0.0
         *   all in [k, right] >=  0.0
         *
         * Pointer k is the first index of ?-part.
         */
    for (int k = left, p = left - 1; ++k <= right; ) {
      float ak = a[k];
      if (ak != 0.0f) {
        break;
      }
      if (Float.floatToRawIntBits(ak) < 0) { // ak is -0.0f
        a[k] = 0.0f;
        a[++p] = -0.0f;
      }
    }
  }

  /**
   * Sorts the specified range of the array.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  private static void doSort(float[] a, int left, int right,
      float[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          float t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    float[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new float[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      float[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(float[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          float ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          float a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        float last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      float t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      float t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      float t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      float t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      float pivot1 = a[e2];
      float pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        float ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          float ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = a[great];
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      float pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        float ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = a[great];
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }

  /**
   * Sorts the specified range of the array using the given
   * workspace array slice if possible for merging
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  static void sort(double[] a, int left, int right,
      double[] work, int workBase, int workLen) {
        /*
         * Phase 1: Move NaNs to the end of the array.
         */
    while (left <= right && Double.isNaN(a[right])) {
      --right;
    }
    for (int k = right; --k >= left; ) {
      double ak = a[k];
      if (ak != ak) { // a[k] is NaN
        a[k] = a[right];
        a[right] = ak;
        --right;
      }
    }

        /*
         * Phase 2: Sort everything except NaNs (which are already in place).
         */
    doSort(a, left, right, work, workBase, workLen);

        /*
         * Phase 3: Place negative zeros before positive zeros.
         */
    int hi = right;

        /*
         * Find the first zero, or first positive, or last negative element.
         */
    while (left < hi) {
      int middle = (left + hi) >>> 1;
      double middleValue = a[middle];

      if (middleValue < 0.0d) {
        left = middle + 1;
      } else {
        hi = middle;
      }
    }

        /*
         * Skip the last negative value (if any) or all leading negative zeros.
         */
    while (left <= right && Double.doubleToRawLongBits(a[left]) < 0) {
      ++left;
    }

        /*
         * Move negative zeros to the beginning of the sub-range.
         *
         * Partitioning:
         *
         * +----------------------------------------------------+
         * |   < 0.0   |   -0.0   |   0.0   |   ?  ( >= 0.0 )   |
         * +----------------------------------------------------+
         *              ^          ^         ^
         *              |          |         |
         *             left        p         k
         *
         * Invariants:
         *
         *   all in (*,  left)  <  0.0
         *   all in [left,  p) == -0.0
         *   all in [p,     k) ==  0.0
         *   all in [k, right] >=  0.0
         *
         * Pointer k is the first index of ?-part.
         */
    for (int k = left, p = left - 1; ++k <= right; ) {
      double ak = a[k];
      if (ak != 0.0d) {
        break;
      }
      if (Double.doubleToRawLongBits(ak) < 0) { // ak is -0.0d
        a[k] = 0.0d;
        a[++p] = -0.0d;
      }
    }
  }

  /**
   * Sorts the specified range of the array.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param work a workspace array (slice)
   * @param workBase origin of usable space in work array
   * @param workLen usable size of work array
   */
  private static void doSort(double[] a, int left, int right,
      double[] work, int workBase, int workLen) {
    // Use Quicksort on small arrays
    if (right - left < QUICKSORT_THRESHOLD) {
      sort(a, left, right, true);
      return;
    }

        /*
         * Index run[i] is the start of i-th run
         * (ascending or descending sequence).
         */
    int[] run = new int[MAX_RUN_COUNT + 1];
    int count = 0;
    run[0] = left;

    // Check if the array is nearly sorted
    for (int k = left; k < right; run[count] = k) {
      if (a[k] < a[k + 1]) { // ascending
        while (++k <= right && a[k - 1] <= a[k]) {
          ;
        }
      } else if (a[k] > a[k + 1]) { // descending
        while (++k <= right && a[k - 1] >= a[k]) {
          ;
        }
        for (int lo = run[count] - 1, hi = k; ++lo < --hi; ) {
          double t = a[lo];
          a[lo] = a[hi];
          a[hi] = t;
        }
      } else { // equal
        for (int m = MAX_RUN_LENGTH; ++k <= right && a[k - 1] == a[k]; ) {
          if (--m == 0) {
            sort(a, left, right, true);
            return;
          }
        }
      }

            /*
             * The array is not highly structured,
             * use Quicksort instead of merge sort.
             */
      if (++count == MAX_RUN_COUNT) {
        sort(a, left, right, true);
        return;
      }
    }

    // Check special cases
    // Implementation note: variable "right" is increased by 1.
    if (run[count] == right++) { // The last run contains one element
      run[++count] = right;
    } else if (count == 1) { // The array is already sorted
      return;
    }

    // Determine alternation base for merge
    byte odd = 0;
    for (int n = 1; (n <<= 1) < count; odd ^= 1) {
      ;
    }

    // Use or create temporary array b for merging
    double[] b;                 // temp array; alternates with a
    int ao, bo;              // array offsets from 'left'
    int blen = right - left; // space needed for b
    if (work == null || workLen < blen || workBase + blen > work.length) {
      work = new double[blen];
      workBase = 0;
    }
    if (odd == 0) {
      System.arraycopy(a, left, work, workBase, blen);
      b = a;
      bo = 0;
      a = work;
      ao = workBase - left;
    } else {
      b = work;
      ao = 0;
      bo = workBase - left;
    }

    // Merging
    for (int last; count > 1; count = last) {
      for (int k = (last = 0) + 2; k <= count; k += 2) {
        int hi = run[k], mi = run[k - 1];
        for (int i = run[k - 2], p = i, q = mi; i < hi; ++i) {
          if (q >= hi || p < mi && a[p + ao] <= a[q + ao]) {
            b[i + bo] = a[p++ + ao];
          } else {
            b[i + bo] = a[q++ + ao];
          }
        }
        run[++last] = hi;
      }
      if ((count & 1) != 0) {
        for (int i = right, lo = run[count - 1]; --i >= lo;
            b[i + bo] = a[i + ao]
            ) {
          ;
        }
        run[++last] = right;
      }
      double[] t = a;
      a = b;
      b = t;
      int o = ao;
      ao = bo;
      bo = o;
    }
  }

  /**
   * Sorts the specified range of the array by Dual-Pivot Quicksort.
   *
   * @param a the array to be sorted
   * @param left the index of the first element, inclusive, to be sorted
   * @param right the index of the last element, inclusive, to be sorted
   * @param leftmost indicates if this part is the leftmost in the range
   */
  private static void sort(double[] a, int left, int right, boolean leftmost) {
    int length = right - left + 1;

    // Use insertion sort on tiny arrays
    if (length < INSERTION_SORT_THRESHOLD) {
      if (leftmost) {
                /*
                 * Traditional (without sentinel) insertion sort,
                 * optimized for server VM, is used in case of
                 * the leftmost part.
                 */
        for (int i = left, j = i; i < right; j = ++i) {
          double ai = a[i + 1];
          while (ai < a[j]) {
            a[j + 1] = a[j];
            if (j-- == left) {
              break;
            }
          }
          a[j + 1] = ai;
        }
      } else {
                /*
                 * Skip the longest ascending sequence.
                 */
        do {
          if (left >= right) {
            return;
          }
        } while (a[++left] >= a[left - 1]);

                /*
                 * Every element from adjoining part plays the role
                 * of sentinel, therefore this allows us to avoid the
                 * left range check on each iteration. Moreover, we use
                 * the more optimized algorithm, so called pair insertion
                 * sort, which is faster (in the context of Quicksort)
                 * than traditional implementation of insertion sort.
                 */
        for (int k = left; ++left <= right; k = ++left) {
          double a1 = a[k], a2 = a[left];

          if (a1 < a2) {
            a2 = a1;
            a1 = a[left];
          }
          while (a1 < a[--k]) {
            a[k + 2] = a[k];
          }
          a[++k + 1] = a1;

          while (a2 < a[--k]) {
            a[k + 1] = a[k];
          }
          a[k + 1] = a2;
        }
        double last = a[right];

        while (last < a[--right]) {
          a[right + 1] = a[right];
        }
        a[right + 1] = last;
      }
      return;
    }

    // Inexpensive approximation of length / 7
    int seventh = (length >> 3) + (length >> 6) + 1;

        /*
         * Sort five evenly spaced elements around (and including) the
         * center element in the range. These elements will be used for
         * pivot selection as described below. The choice for spacing
         * these elements was empirically determined to work well on
         * a wide variety of inputs.
         */
    int e3 = (left + right) >>> 1; // The midpoint
    int e2 = e3 - seventh;
    int e1 = e2 - seventh;
    int e4 = e3 + seventh;
    int e5 = e4 + seventh;

    // Sort these elements using insertion sort
    if (a[e2] < a[e1]) {
      double t = a[e2];
      a[e2] = a[e1];
      a[e1] = t;
    }

    if (a[e3] < a[e2]) {
      double t = a[e3];
      a[e3] = a[e2];
      a[e2] = t;
      if (t < a[e1]) {
        a[e2] = a[e1];
        a[e1] = t;
      }
    }
    if (a[e4] < a[e3]) {
      double t = a[e4];
      a[e4] = a[e3];
      a[e3] = t;
      if (t < a[e2]) {
        a[e3] = a[e2];
        a[e2] = t;
        if (t < a[e1]) {
          a[e2] = a[e1];
          a[e1] = t;
        }
      }
    }
    if (a[e5] < a[e4]) {
      double t = a[e5];
      a[e5] = a[e4];
      a[e4] = t;
      if (t < a[e3]) {
        a[e4] = a[e3];
        a[e3] = t;
        if (t < a[e2]) {
          a[e3] = a[e2];
          a[e2] = t;
          if (t < a[e1]) {
            a[e2] = a[e1];
            a[e1] = t;
          }
        }
      }
    }

    // Pointers
    int less = left;  // The index of the first element of center part
    int great = right; // The index before the first element of right part

    if (a[e1] != a[e2] && a[e2] != a[e3] && a[e3] != a[e4] && a[e4] != a[e5]) {
            /*
             * Use the second and fourth of the five sorted elements as pivots.
             * These values are inexpensive approximations of the first and
             * second terciles of the array. Note that pivot1 <= pivot2.
             */
      double pivot1 = a[e2];
      double pivot2 = a[e4];

            /*
             * The first and the last elements to be sorted are moved to the
             * locations formerly occupied by the pivots. When partitioning
             * is complete, the pivots are swapped back into their final
             * positions, and excluded from subsequent sorting.
             */
      a[e2] = a[left];
      a[e4] = a[right];

            /*
             * Skip elements, which are less or greater than pivot values.
             */
      while (a[++less] < pivot1) {
        ;
      }
      while (a[--great] > pivot2) {
        ;
      }

            /*
             * Partitioning:
             *
             *   left part           center part                   right part
             * +--------------------------------------------------------------+
             * |  < pivot1  |  pivot1 <= && <= pivot2  |    ?    |  > pivot2  |
             * +--------------------------------------------------------------+
             *               ^                          ^       ^
             *               |                          |       |
             *              less                        k     great
             *
             * Invariants:
             *
             *              all in (left, less)   < pivot1
             *    pivot1 <= all in [less, k)     <= pivot2
             *              all in (great, right) > pivot2
             *
             * Pointer k is the first index of ?-part.
             */
      outer:
      for (int k = less - 1; ++k <= great; ) {
        double ak = a[k];
        if (ak < pivot1) { // Move a[k] to left part
          a[k] = a[less];
                    /*
                     * Here and below we use "a[i] = b; i++;" instead
                     * of "a[i++] = b;" due to performance issue.
                     */
          a[less] = ak;
          ++less;
        } else if (ak > pivot2) { // Move a[k] to right part
          while (a[great] > pivot2) {
            if (great-- == k) {
              break outer;
            }
          }
          if (a[great] < pivot1) { // a[great] <= pivot2
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // pivot1 <= a[great] <= pivot2
            a[k] = a[great];
          }
                    /*
                     * Here and below we use "a[i] = b; i--;" instead
                     * of "a[i--] = b;" due to performance issue.
                     */
          a[great] = ak;
          --great;
        }
      }

      // Swap pivots into their final positions
      a[left] = a[less - 1];
      a[less - 1] = pivot1;
      a[right] = a[great + 1];
      a[great + 1] = pivot2;

      // Sort left and right parts recursively, excluding known pivots
      sort(a, left, less - 2, leftmost);
      sort(a, great + 2, right, false);

            /*
             * If center part is too large (comprises > 4/7 of the array),
             * swap internal pivot values to ends.
             */
      if (less < e1 && e5 < great) {
                /*
                 * Skip elements, which are equal to pivot values.
                 */
        while (a[less] == pivot1) {
          ++less;
        }

        while (a[great] == pivot2) {
          --great;
        }

                /*
                 * Partitioning:
                 *
                 *   left part         center part                  right part
                 * +----------------------------------------------------------+
                 * | == pivot1 |  pivot1 < && < pivot2  |    ?    | == pivot2 |
                 * +----------------------------------------------------------+
                 *              ^                        ^       ^
                 *              |                        |       |
                 *             less                      k     great
                 *
                 * Invariants:
                 *
                 *              all in (*,  less) == pivot1
                 *     pivot1 < all in [less,  k)  < pivot2
                 *              all in (great, *) == pivot2
                 *
                 * Pointer k is the first index of ?-part.
                 */
        outer:
        for (int k = less - 1; ++k <= great; ) {
          double ak = a[k];
          if (ak == pivot1) { // Move a[k] to left part
            a[k] = a[less];
            a[less] = ak;
            ++less;
          } else if (ak == pivot2) { // Move a[k] to right part
            while (a[great] == pivot2) {
              if (great-- == k) {
                break outer;
              }
            }
            if (a[great] == pivot1) { // a[great] < pivot2
              a[k] = a[less];
                            /*
                             * Even though a[great] equals to pivot1, the
                             * assignment a[less] = pivot1 may be incorrect,
                             * if a[great] and pivot1 are floating-point zeros
                             * of different signs. Therefore in float and
                             * double sorting methods we have to use more
                             * accurate assignment a[less] = a[great].
                             */
              a[less] = a[great];
              ++less;
            } else { // pivot1 < a[great] < pivot2
              a[k] = a[great];
            }
            a[great] = ak;
            --great;
          }
        }
      }

      // Sort center part recursively
      sort(a, less, great, false);

    } else { // Partitioning with one pivot
            /*
             * Use the third of the five sorted elements as pivot.
             * This value is inexpensive approximation of the median.
             */
      double pivot = a[e3];

            /*
             * Partitioning degenerates to the traditional 3-way
             * (or "Dutch National Flag") schema:
             *
             *   left part    center part              right part
             * +-------------------------------------------------+
             * |  < pivot  |   == pivot   |     ?    |  > pivot  |
             * +-------------------------------------------------+
             *              ^              ^        ^
             *              |              |        |
             *             less            k      great
             *
             * Invariants:
             *
             *   all in (left, less)   < pivot
             *   all in [less, k)     == pivot
             *   all in (great, right) > pivot
             *
             * Pointer k is the first index of ?-part.
             */
      for (int k = less; k <= great; ++k) {
        if (a[k] == pivot) {
          continue;
        }
        double ak = a[k];
        if (ak < pivot) { // Move a[k] to left part
          a[k] = a[less];
          a[less] = ak;
          ++less;
        } else { // a[k] > pivot - Move a[k] to right part
          while (a[great] > pivot) {
            --great;
          }
          if (a[great] < pivot) { // a[great] <= pivot
            a[k] = a[less];
            a[less] = a[great];
            ++less;
          } else { // a[great] == pivot
                        /*
                         * Even though a[great] equals to pivot, the
                         * assignment a[k] = pivot may be incorrect,
                         * if a[great] and pivot are floating-point
                         * zeros of different signs. Therefore in float
                         * and double sorting methods we have to use
                         * more accurate assignment a[k] = a[great].
                         */
            a[k] = a[great];
          }
          a[great] = ak;
          --great;
        }
      }

            /*
             * Sort left and right parts recursively.
             * All elements from center part are equal
             * and, therefore, already sorted.
             */
      sort(a, left, less - 1, leftmost);
      sort(a, great + 1, right, false);
    }
  }
}
